Tuesday, May 28, 2019

Confirmation that the World card is based on the throne scene in Revelation

The earliest known list of the Tarot trumps comes from the anonymous Sermones de ludo cum aliis ("Discourses on a game played with others"), published in Venice in the late 15th century, probably by a Dominican monk. It follows the Ferrara-Venice ordering of the trumps, which differs in several respects from the now-standard Milan-Marseille ordering. The author includes brief parenthetical comments on some of the trumps, including the World.

The 21st item on the list is (modernizing the spelling) "Il mondo, cioè Dio Padre" -- "The world, that is to say, God the Father."

As detailed in my very long post The Throne and the World, the World card derives from "Christ in majesty" iconography, which in turn is based on the description of God the Father on his throne in Revelation 4-5. That this 15th century writer simply equates the World with God the Father is strong evidence for this connection. It also shows that that version of the World card is older than might otherwise be supposed. The oldest surviving World cards have very different images; for example, the Visconti-Sforza, shows the earth being supported by two winged putti -- an image completely unrelated to the Marseille card or to biblical throne scenes. The list in Sermones is evidence that the World as God was already established in 15th-century Italy and was not a Marseille innovation.

The orientation of ROTA

I found this diagram in Éliphas Lévi's Rituel de la Haute Magie, included apropos of nothing, and with no caption or explanation given.

I don't feel like searching through Agrippa or whoever for the meaning of the various sigils around the edge of the picture, but the main theme is a familiar one: the wheel with ROTA/TARO written around its circumference, a symbol created by Guillaume Postel and much used by Lévi. The four suits of the Tarot also figure in the diagram. The wand (on the right) has the form of a double-headed Wenchang pen, as seen in the Rider-Waite deck, apparently yet another instance of Lévi's influence on Waite. The sword and cup are easily identifiable, and I suppose that the suit of coins is, as in Waite, represented by the "pentacle" -- which, as Lévi uses the word, need not take the form of a five-pointed star. (To break the connection with the numerical prefix penta-, Lévi prefers the nonstandard spelling pantacle, an innovation later followed by Aleister Crowley, with whom it is now primarily associated.)

What caught my attention was the apparent mismatch between the four suits and the four letters. The letter O is paired with the sword, but it resembles a coin. A sword has the form of a cross and should therefore be paired with T. The A used here by Lévi, like the one that appears on the Rider-Waite Wheel of Fortune card, has a flat or rounded top rather than a pointed one, so that when it is turned upside down it looks like a cross-section of a cup with some liquid in it. That leaves the letter R to be paired with the wand, which it does not particularly resemble. However, Spanish and Italian versions of that suit -- a heavy-headed club or mace, not a wand -- do suggest the Greek letter P, and the Sicilian asso di mazze even bears a certain resemblance to an R.

In an arrangement independently arrived at by Whitley Strieber in his book The Path, Lévi puts the cup at the bottom, the coin/pentacle at the top, the sword on the left, and the wand/club on the right. If we rotate our ROTA 90 degrees to the right, the upside-down A (which resembles a cup) will be lined up with the cup, and the O with the coin. Unfortunately, the sword has to be switched with the wand to make those correspondences work.

However, if we rotate the wheel again, so that the A is at the top, we can keep the Lévi/Strieber orientation of the suits. O works for the cup since it is round, and A (which in this case should be written in the usual angular fashion) matches the pentacle. Another word for a pentagram is pentalpha because it consists of five letter A's in different orientations. This mapping also means that the word ROTA gives the suits in their conventional order: wands, cups, swords, pentacles.

All that having been said, I still find that the orientation I prefer is the one with R at the top, matching both the Chrismon of Saint Ambrose (discussed in relation to the Wheel of Fortune here) and the cruciform halo of Christ in the Basilique Saint-Sernin de Toulouse (discussed in relation to the World card here).

(Note that the Christ carving shown is actually a modern one by Jonathan Pageau, based on the original in Toulouse. I chose it because the three letters are more clearly legible than they are in available photos of the original carving. Note also that the letter that looks like W is actually a lowercase omega, corresponding to O.)

In fact, of the four possible orientations of the ROTA, the only one I can't think of any good reason for is the one actually used by Lévi and Waite, with T at the top!

Sunday, May 26, 2019

The rhyme burden of various poetic forms

"Rhyme burden" is a number indicating, on average, how many other feet each foot in a poem must rhyme with.

For example, in a Shakespearean sonnet, each line has five feet, and the final foot of each line rhymes with the final foot of one of the other lines. The other feet need not rhyme with anything. We can express this pattern as 0 0 0 0 1. Averaging those numbers gives us a rhyme burden of 1/5 (0.2) for this type of verse.

The terza rima of the Divine Comedy also has five feet per line, and only the final foot has to rhyme with anything. However, each line of terza rima must rhyme with two other lines (0 0 0 0 2), so its rhyme burden is 2/5 (0.4), twice that of a Shakespearean sonnet. As far as rhyme goes, writing terza rima is about twice as hard as writing a Shakespearean sonnet.

Even terza rima, though, is not nearly as hard to write as a good limerick. A limerick consists of 13 feet, the rhyme requirements of which are 0 0 2 0 0 2 0 1 0 1 0 0 2. Its rhyme burden, then, is 8/13 (about 0.615).

Here are the rhyme burden figures for various poetic forms, as well as for a handful of specific rhyme-dense poems. Lines which repeat previous lines (such as the final line of "Stopping by Woods on a Snowy Evening") are not included in the calculations.

  • Blank verse: 0
  • Ballad, fourteeners: 0.143
  • Hexameter couplets: 0.167
  • Pentameter couplets, Shakeseparean sonnet: 0.2
  • Tetrameter couplets: 0.25
  • Common meter: 0.286
  • Trimeter couplets: 0.333
  • Ottava rima (Don Juan): 0.35
  • "Sweet Baby James": 0.357 
  • Terza rima (Divine Comedy), "The Road Not Taken": 0.4
  • Petrarchan sonnet (CDECDE sestet), Spenserian sonnet: 0.429
  • Spenserian stanzas (Faerie Queene): 0.435
  • Dimeter couplets: 0.5
  • Petrarchan sonnet (CDCDCD sestet): 0.514
  • "The Witch" (Yeats): 0.533
  • "Leviathan": 0.6
  • Limerick: 0.615
  • "Litany Against Fear": 0.625
  • "Fire and Ice": 0.667
  • "Stopping by Woods on a Snowy Evening": 0.7
  • Monometer couplets ("We Real Cool"): 1
  • Villanelle ("Do not go gentle into that good night"): 1.108

(The two linked poems are my own work, original in form but not in content. They are adaptations of existing poems to new, very complicated rhyme schemes, created as experiments to see whether such schemes were usable.)

Friday, May 24, 2019

Lacrimae lunae

As I've mentioned before, I've been rereading John Opsopaus's Guide to the Pythagorean Tarot these days. Yesterday I started the chapter on the Moon card. It begins with a description of Opsopaus's version of that trump, including this:
We are looking from the edge of a dark sea towards its shore, which is lit by the narrowest crescent of a young, pale yellow moon shining in the dark blue sky. Glowing tear drops (fifteen white, fifteen reddish) fall in three streams (five reddish and five white each) from the recumbent crescent, which is open to the upper left; its dark face is barely visible.
Here is detail of the card in question, showing the red and white teardrops.

Later the same day, I was teaching a beginning-level English class for children. Their textbook includes the following illustration.

Checking each student's book to make sure the accompanying exercise had been done correctly, I was surprised to see that one of the students had (for no apparent reason) used a red pen to color in exactly half of the white water drops in the picture, in the same alternating red-white pattern seen on Opsopaus's Moon card.

(As a further coincidence, in the textbook illustration, too, "we are looking from the edge of a dark sea towards its shore"; and the twin girls in the illustration echo the Moon card's theme of doubleness -- two mountains, two towers, two dogs, etc.)

I'm not sure whether to consider this just a striking coincidence or a case of unconscious telepathy. It's not the first time a student has written or drawn some improbable thing I had been thinking of.

Fire and ice

On the way home from work, the thought suddenly came to me: You know, I should post something about the first "synchronicity" I ever noticed, the one that first caught my attention and made me think, "I should keep a record of these things."

I can still remember it quite clearly. I was approximately 12 years of age and had just read -- I cannot remember why or in what context -- a sermon by a Mormon leader that quoted, with reference to sexual morality, the first four lines of Robert Frost's "Fire and Ice":
Some say the world will end in fire,
Some say in ice.
From what I’ve tasted of desire
I hold with those who favor fire.
Searching lds.org for "some say in ice" turns up exactly one hit, so I think the talk I read must have been "Souls, Symbols, and Sacraments" by Jeffrey R. Holland (qv).

Less than an hour later, I picked up a popular science book I had been reading -- Carl Sagan, perhaps, or some similar writer (I haven't been able to track it down) -- and, after a few minutes of reading, found that it quoted the same four lines of the same poem, this time with reference to the physical heat-death of the universe. The timing, the two completely different contexts in which the poem was used, and the two writers' independent decisions to quote only the first half of what is after all an extremely short poem -- all this had seemed too much to ascribe to coincidence. Not that I had any other explanation.


Anyone who has taken an interest in such things will have discovered the law, "Speak of the synchronicity fairies, and they will appear."

Having just been remembering that "Fire and Ice" synchronicity from decades ago, I arrived home to find my wife watching some sort of true-crime docudrama on TV. The scene was a Halloween party, and one of the guests was dressed as a gypsy fortune-teller, sitting at a table with a crystal ball and some cards spread out in front of her. These were not tarot cards, but almost looked more like Magic: The Gathering or something of that nature. The camera zoomed in briefly such that one, and only one, of these cards was clearly visible. It bore the title "Fire and Ice." Some minutes later, the camera once again showed the cards -- from a different angle, but still only "Fire and Ice" was legible. Nothing was said about the cards, and they didn't play any role in the story as it unfolded; they were apparently there just to set the scene and establish a suitably spooky atmosphere. (Trying to find this card on Google has turned up only an MTG card called "Sword of Fire and Ice," but I'm sure the title was simply "Fire and Ice," with no sword.)

Monday, May 13, 2019

Stalking the wild asparagus

Westerners living in Taiwan are much in demand as extras on TV, and I recently received a job offer as a "soldier on a battleship" in a historical drama. I found this portion of the application form pretty funny.

Apparently, if you want non-vegetarian food, you're on your own!

(In fact, 葷食 just means an ordinary, non-Buddhist diet, including such things as meat and onions. "Foraging" is how Google Translate renders it.)

Wednesday, May 8, 2019

Is there any rhyme or reason to the Petit Lenormand?

The Petit Lenormand is a deck of 36 cards used for divination. Each card has an image (much simpler and more straightforward than those of the Tarot) such as a dog, a book, a tree, etc., and each is associated with a number, from 1 to 36, and with a playing card from the 36-card piquet deck. (Modern piquet uses a 32-card deck, but in the 16th century it was played with 36 cards -- standard French-suited playing cards with ranks 2 through 5 removed. The modern piquet deck removes the sixes as well.) Here's an example of what the cards look like.

And here is a table of the Petit Lenormand cards according to rank and suit. The parenthetical signs after some of the card titles indicate which cards are generally considered to be positive or negative; those without signs are neutral.

How on earth was this arrangement arrived at? I've spent some time trying to winkle out hidden patterns, but so far as I have been able to determine, the combinations of number, playing card, and image are truly random. The only pattern evident is that positive and negative cards are not randomly distributed. There are no negative Spades or Hearts and no positive Clubs; Diamonds is the only suit to contain both positive and negative cards.

The pairing of the images with playing cards appears to be unrelated to the traditional meanings of those cards in cartomancy. For example, the Ace of Spades (traditionally "death") is paired with the Woman, while the Coffin is paired with the Nine of Diamonds (traditionally "profit"). The Queen of Spades, universally considered a card of ill omen, is given a positive meaning. Spades in general are considered an unlucky suit, but the Petit Lenormand associates Spades only with positive and neutral images. Black suits are traditionally masculine and red suits feminine, but the Man and Woman cards in the Petit Lenormand reverse that association.

Nor, if the playing cards are set to one side, does there seem to be any pattern in the numbering of the images. If the cards are listed in order from 1 to 36, no overall pattern is evident. Man and Woman are together, as are Sun and Moon, but that's about it. Traditional meanings of the numbers themselves also seem to have been ignored. For example, even numbers are traditionally considered feminine, and the number 28 particularly so because of its association with the moon and the menstrual cycle -- but 28 is assigned to the Man. The unlucky number 13 is given a positive meaning.


The Petit Lenormand is inherently less interesting than the Major Aracana of the Tarot because its symbols are so simple. This is true even where there is overlap between the two decks. Where the Moon card of the Tarot is an enigmatic scene featuring towers, dogs, a pool of water, and a crayfish, its Petit Lenormand counterpart is just the moon (and an Eight of Hearts). On the other hand, the Petit Lenormand images are considerably more interesting than the (pre-Waite, non-scenic) Tarot pips -- a rather unpromising symbol set consisting of one sword, two swords, three swords, four swords, five swords, etc.

To me, a big part of the interest of such a system as the Petit Lenormand is that it represents a sort of ontology of life. Implicit in its intended use as a fortune-telling system is that any significant life event or situation can be represented by one of the cards or a combination of them. It's interesting to see what kinds of symbols are selected for such an attempted "alphabet of life." (Another such system would be the Alethiometer symbols of Philip Pullman's novels -- also a set of 36 simple images, with considerable overlap with the Petit Lenormand.)

Monday, May 6, 2019

Changing the future and changing the past

In a recent post, Bruce Charlton asks "Can the past be changed?" -- and answers, "Obviously not," going on to pronounce the contrary opinion "demonic." Since I have been guilty of entertaining a version of this doctrine from the pit of hell (see this post), I thought I would revisit the idea.


The first matter of business is to establish exactly what is meant by change. As a simple example of a change, consider my marital status, which changed in the latter part of 2010. Prior to that date, I was not married; after that date, I was and am. That's what change means: that a given proposition ("William James Tychonievich is married") is/was/will be true at some points in time and false at others.

We can represent this change graphically by means of a colored line. The dimension represented by the line is "time," with the past to the left and the future to the right, and the color of any given point on the line represents my marital status at that point in time (blue for single, gold for married). Below is a portion of such a timeline, covering the years from 2009 to 2020.

Fig. 1

We want to consider the idea of changing the future and the past, so this timeline is inadequate, giving no indication of which points on the line are past and which are future. We need to add something to indicate that the present moment is -- well, of course it's a moving target, changing even as I type this sentence, but this is a pretty low-resolution timeline, so "about a third of the way through 2019" will be good enough for our purposes. (If you should happen to be reading this post at a significantly later date, please be so good as to proceed on the counterfactual-to-you assumption that the present moment is indeed in that general vicinity.) Let us modify our timeline by reserving the bright colors used in Fig. 1 for past points in time and representing future points by paler versions of the same colors, like so:

Fig. 2

There are now two points on the timeline where the color changes. The point where it changes from blue to gold represents the event of my marriage. To the left of that point, I was single; to the right, I was, am, and will be married. The point where the line changes from bright to pale represents the present moment. Everything to the left of that point is past, and everything to the right of it is future.

Now, we have already established that my marriage in 2010 constitutes an example of a change, and our timeline above locates that change to the left of the present moment -- that is, in the past. Is this, then, what we mean by "changing the past? Obviously not -- but why not, and what do we mean?

Well, the natural answer is something like this: The change in question occurred in 2010 -- which means that at that time, 2010 was not in the past but was the present year. If what happened in 2010 were to change now, that would be what we mean by "changing the past." But this introduces a distinction between 2010-in-2010 and 2010-now which cannot be represented on a one-dimensional timeline. Such time designations require two coordinates -- (2010, 2010), (2010, 2019) -- which means our simple timeline must be expanded into a two-dimensional "timeplane" of the type pioneered by J. W. Dunne and discussed in my post "The present now will later be past."

The title of that post, taken from the Bob Dylan Song "The Times They Are a-Changin'," was chosen because, while it seems very obviously true, it implicitly assumes a two-dimensional model of time. A simple timeline, like Fig. 2 above, can represent past, present, and future, but not the idea that "the present now will later be past." The very phrase "will later be past" describes the same state of affairs as being future in one sense and past in another -- which requires a rectangular coordinate system comprising two perpendicular timelines.

Fig. 3

Now I know from experience -- my own included -- that this is point at which readers' eyes start to glaze over, but I'm afraid there's just no avoiding these diagrams. I can only ask for the reader's patience and do my best to explain. The color of each point on the timeplane in Fig. 3 represents a proposition regarding my marital status: The hue represents the content of the proposition (blue for single, gold for married), and the tint represents its tense (pure colors for past, light colors for future). Each point is located in two different temporal dimensions: The x-axis ("object time") represents the time the proposition refers to, and the y-axis ("meta-time") represent the time at which the proposition is true.

I've marked two (arbitrarily selected) regions on the plane "A" and "B," respectively, in order to use them as examples. They represent the following meta-propositions:
A: In 2010, the proposition "WJT will be married in 2012" was true.
B: In 2014, the proposition "WJT was married in 2012" was true. 
For completeness, we really ought to indicate the tense of the meta-proposition as well. Fig. 4, below, is so modified as to express this. Solid colors (such as were used in Fig. 3) represent meta-past, and stippling represents meta-future.

Fig. 4

The region marked "C" in Fig. 4 represents the following meta-proposition:
In 2020, the proposition "WJT was married in 2011" will be true.
The "was" in the object proposition is indicated by the use of a pure color as opposed to a tint, and the "will be" of the meta-proposition is indicated by stippling.

The red dot in Fig. 4 marks the place where the true present may be found. (Or at least, this was true when I wrote it, about a third of the way through the year 2019.) When we say, "2019 is the present year," the word "present" corresponds to the diagonal line separating pure colors from tints, and the present-tense verb "is" corresponds to the horizontal line separating solid colors from stippling. The intersection of those two lines, marked with the red dot, is "the present now." Dylan's statement that "the present now will later be past" means that if we start at the red dot ("the present now") and move vertically down into the stippled region ("will later be"), we find a pure color ("past") rather than a tint.

Take a minute to digest that. I want to be sure the meaning of these timeplane diagrams is clear before proceeding.

Now look back at the region marked "A" in Fig. 3 and the meta-proposition to which it corresponds: "In 2010, the proposition 'WJT will be married in 2012' was [already] true." And consider this: If I were to extend my timeplane diagram to cover a wider range of past times, there would be a region on that diagram corresponding to the meta-proposition "In 4000 BC, the proposition 'WJT will be married in 2012' was already true." This is fatalism, of the unassailable variety spelled out by Richard Taylor (whose argument I discuss here) -- unassailable because it does not depend on the doctrine of causal determinism. From the mere assumption that all possible statements about the future are (already) either true or false, and that their truth-value cannot change, it follows that all is fated, that whatever happens is inevitable.

 To escape Taylorian fatalism, it is necessary to believe that we can change the future -- an idea which is common enough in naive discourse, and which our two-dimensional timeplane allows us to model. Let us modify our diagram, then. Instead of assuming (as Fig. 4 does) that my getting married in late 2010 is something that was always going to happen, something that was already written in the book of fate hundreds of years before my birth, or as far back as you care to imagine -- instead of assuming that, let's assume instead that I wasn't going to get married on that date, not until I actually made the decision to do so. Let's assume that my decision, rather than being just another step in the inevitable unfolding of fate, actually decided something, literally changed the future. And let's further assume (as seems reasonable) that this future-altering decision was made some months before the actual event of the marriage.

Fig. 5

The black dot on the timeplane in Fig. 5 represents the moment I exercised my agency and made the fateful decision (which, I need hardly mention, is entirely different from a fated decision, the latter being a contradiction in terms and no decision at all).

The diagonal line that passes through the black and red dots, and divides the pure colors on the left from the tints on the right, represents the timeline of my life as I experience it, as a succession of object-time "presents." The horizontal line that passes through the red dot, and divides the solid colors from the stippling, represents the meta-time present. (The object-time present is a point; the meta-time present is a line.) The intersection of these two lines divides the plane into four quadrants, representing (clockwise from the upper left), what had happened (solid pure colors), what was going to happen (solid tints), what will be going to happen (stippled tints), and what will have happened (stippled pure colors).


The diagonal line -- my life as I experience it -- is exactly the same in Fig. 4 (where the future is fated) and in Fig. 5 (where it can change). It would appear, then, that there can be no empirical evidence for the one model or the other, no possible experience that would be more consistent with the one than with the other. Choosing one over the other would be a metaphysical assumption, not a conclusion from evidence.

However, that may not be entirely true. There is considerable evidence (see J. W. Dunne's Experiment with Time for starters) that, while the attention is generally confined to the point-present represented by the red dot, it can sometimes extend to other regions of the linear meta-time present, especially during dreams or similar states of relaxed or diffuse attention. In such states, we have access to the object-time future (precognition) and past (retrocognition) -- at least as they exist at the meta-time present. Under Taylorian fatalism (as diagrammed in Fig. 4), the content of object time does not vary across meta-time; the only meta-time change is that of tense (as the future becomes the past), so whatever future events are perceived through genuine Dunnean precognition will infallibly come to pass when the future times in question become present. There would be no possibility of seeing the future and then changing your behavior as a result of what you see, with the result that the foreseen event is averted. This is precisely what fatalism -- of the sort seen in the Greek myths, for example -- means. Cassandra's prophetic warnings are ignored and have no power to prevent the events they foretell. The prophecies regarding Oedipus are not ignored, but the very attempt to thwart them leads to their fulfillment. Either way, fate ineluctably plays out.

In the model where the future can be changed (as diagrammed in Fig. 5), even true precognitions need not necessarily come true. For example, look back at Fig. 5 and imagine that in 2009 (in both object time and meta-time -- that is, at a point on the diagonal line) I had a precognitive vision of 2011. Since such a vision would be of object-time 2011 at meta-time 2009, I would see myself as still single at that date. However, by the time object-time 2011 becomes the meta-time present, it will already have changed, so that the 2011 I experience will be different from the 2011 I foresaw. Nonetheless, what I foresaw was true. (If that seems like a contradiction, consider this analogy. I turn on the TV to the weather channel and discover that it is sunny in Taipei. I then get in my car, drive to Taipei, and upon my arrival find that it is raining. But what I saw on TV was true.) Instances of true precognition that do not come true would be evidence that the future can be changed.

The problem, of course, is that, if a vision or premonition does not come true, there would seem to be no grounds for considering it genuinely precognitive. For example, once in my late teens, at a time when I had no plans to go overseas, I had a very vivid and detailed dream in which I was about 30 and living in Vietnam. I'm 40 now and have never set foot in that particular country. It's possible that my Vietnam dream was genuinely precognitive, revealing what was (at that time) going to happen in the future, but that the future it foretold has since changed because of choices I or others have made. It could also be considered a garbled precognition of what in fact came to pass. (I do live in Asia and have for most of my adult life.) But there's no good reason to believe that, and the simplest explanation is that it was just a dream and not precognitive at all. Certainly such a dream cannot constitute evidence that the future can be changed. Is such evidence possible?

Consider the premise of the Final Destination series of horror movies. The protagonist has a sudden vision of a series of events leading up to all his friends dying horribly in a freak accident. When the foreseen events begin to play out in real life, he panics and manages to prevent his friends from getting on the doomed plane or roller coaster or whatever. Then the freak accident occurs as foreseen, except that his friends are not among those killed by it. Later they all go on to die horribly anyway, in different freak accidents, because "you can't cheat death," but that's not germane to my point here, which is that the originally premonition is clearly a true one even though it does not come to pass exactly as foreseen. When people act on a precognitive warning so that the foreseen event does not happen, but subsequent events make it abundantly clear that it would have happened had they not taken action, that is evidence that the future can be changed.

Such evidence in fact exists. The literature on precognition is full of Final Destination type stories (minus the post-accident bit where everyone dies horribly anyway). Someone has a premonition of being in a plane crash, they cancel their tickets, and then the flight they would have been on crashes. That kind of thing.


What about changing the past? Well, it's a bizarre idea, so our illustrative example will be a little bizarre as well. I must ask the reader to suspend disbelief, ignoring for the moment the question of whether or not such things can really happen. Our question is what it would mean for the past to change, and, supposing it did change, whether there could be any empirical evidence of that change.

Suppose that "originally" I chose not to get married in 2010. Years later, in 2015, I looked back on that choice with regret and said to myself, "I wish I'd married that girl when I had the chance!" A passing genie happened to hear my remark and granted the wish. From that moment, it suddenly became true that I had gotten married in 2010. We can represent this hypothetical story graphically as below, in Fig. 6.

Fig. 6
The black dot on the plane in Fig. 6 indicates the moment at which my wish was granted. Notice that, when the past changes, the present and future change as well, since chains of cause-and-effect run horizontally from left to right across the diagram (i.e., causation is an object-time phenomenon).

Remember that the diagonal line dividing the pure colors from the tints represents my life as I actually experience it, as a succession of presents -- and notice that in the world depicted by Fig. 6, I never actually experience my own wedding or the first several years of my married life. I go directly from being a bachelor to having been married for nearly five years! Surely such an obvious discontinuity in my experience could not possibly go unnoticed, and surely the fact that people's lives don't include such discontinuities is evidence that the past cannot change -- right?

Well, not exactly. Remember that causation is an object-time phenomenon. When object-time 2010 changed in meta-time 2015, all subsequent points in object time also changed as a result of the causal effects of that 2010 wedding. For example, if photos were taken at the wedding, those photos will (after the granting of my wish) still be there in 2015 and after. But if the creation of photos is one of the effects of the wedding, the creation of memories in the minds of the participants is another. If my memories of the past are understood to be effects of those past events in the ordinary sense of that word (i.e., one of the effects of a given past event is an alteration in the state of my brain, which alteration persists through time and constitutes my memory of that event), then my memories at any given point in my life will be of what preceded that point horizontally (i.e., in object time), not diagonally along the line of my actual experience. If the past cannot be changed, the difference is immaterial, since the content of the horizontal and diagonal pasts will be identical. If it can be changed, then as soon as the change has happened, the content of my "original" past is inaccessible to me. When, at the moment marked with the black dot, I suddenly transform from a bachelor into someone who has been married for five years, my memories change as well. I would have no memory of ever having chosen not to get married in 2010, nor of regretting my choice and having my wish granted by a genie. My memory would tell me that I had "always" gotten married in 2010, and all observable effects in the present would also be consistent with that. No evidence that the past had changed would be possible.

What about retrocognition -- "paranormal" direct access to the past, corresponding to precognition and different from ordinary memory? Would that give us access to the "original" past, before it had changed? No, because like precognition, it represents an expansion of attention from the point-present to the linear present of meta-time (represented in the figures by the horizontal line passing through the red dot).


I had originally planned to discuss the so-called "Mandela Effect" -- the phenomenon of memories that don't match documented history (such as many people's memories of Nelson Mandela having died in prison, or of the Berenstain bears being called the Berenstein Bears) -- as possibly representing memories of the past before it was changed, but our two-dimensional time model has no way of accounting for such "memories" (except to say that they are simply errors). That will require us to venture into the even-more-confusing domain of meta-meta-time -- and, this post already being quite long enough, I think I will reserve that discussion (and a discussion of the moral significance of changeable vs. unchangeable pasts, as raised by Bruce Charlton) for the sequel.

Friday, May 3, 2019

Arkansas took control

Once I have misheard the lyrics of a song, my brain can be quite insistent on continuing to hear them that way, even after I have been informed of what they "really" are. For example, despite knowing now that the phrase repeated in the chorus of the David Bowie song "Five Years" is -- as should have been obvious! -- five years, I continue to hear it as bupkis: "Bupkis, that's all we've got. We've got bupkis, what a surprise . . . ." Of course bupkis is a Yiddish-derived Americanism unlikely to have been in Bowie's active vocabulary, and "Five Years" is, you know, the name of the song, but the part of my brain that listens to music remains unconvinced.

Another particularly stubborn mishearing is the beginning of the Moody Blues song "Blue World" -- which, as you may not be aware, begins "Arkansas took control, took control of me." Apparently so many people mishear "Arkansas" as "heart and soul" that the latter version actually made it into the liner notes, an error which has been repeated on roughly 100% of Internet lyrics sites!

Looking at the context, we can easily see that "heart and soul" is an error.
Arkansas took control,
Took control of me.
Paid my dues, spread the news,
Hands across the sea.
Obviously your heart and soul can't take control of you; they are you. Just as obviously, this is about getting involved in some sort of political rannygazoo -- dues-paying and news-spraying not being activities noted for their soulfulness. Since my immersion in the music of the Moody Blues began quite abruptly in September 1992, a few months before Bill Clinton, then governor of Arkansas, was elected president, I naturally associated this political "Arkansas" with him. Never mind that "Blue World" was released in England in 1983, nine years before Clinton's election and 17 years before his party began to be thought of as the "Blue" faction; one can't get too hung up on linearity when it comes to interpreting lyrics.


A further dimension was added to the Arkansas theme by a bluegrass song I first encountered around the same time as the Moody Blues: "Down in the Arkin'," as performed by a local Thompson, Ohio, bluegrass band called Barb and Uncle Dave's Pure Quill on their album There's a Place in Thompson. (It turns out not to be true that everything is on YouTube now.) It consists of a series of doggerel verses, with this refrain, slightly different from the classic Jimmy Driftwood version:
Down in the Arkin', down in the Arkin', down in the Arkin-saw,
The prettiest girls I ever did see were down in the Arkin-saw
For some reason -- perhaps it was the covert influence of the hidden word ark -- I thought of this as being sung by the angels in Genesis 6 who looked down from heaven and "saw the daughters of men, that they were fair" -- hence the reference to pretty girls down in the Arkansas. "Arkansas" then became, in my mind, a name for the corrupt antediluvian world, and the first line of the refrain became "Down in the Ark, and down in the Ark, and down in the Arkansas" -- directly paralleling the Beatles' line "Back in the US, back in the US, back in the USSR."

Just as "US" (the United States) turns out to be the beginning of "USSR" (the enemy of the United States), so "Ark" (of Noah) turns out to be the beginning of "Arkansas" (Noah's enemies). And the line about "the prettiest girls I ever did see" parallels "the Ukraine girls really knock me out" etc. The implication is that the US is not so different from the USSR, and the Ark is really just another Arkansas.

Once "Arkansas" had come to be associated with the world destroyed by the Flood, it was only natural to reinterpret the "Blue World" of the Moody Blues song as a reference to that Flood, a connection that was reinforced by the release a few years later of the heavily advertised movie Waterworld.


At this point, the synchronicity fairies have chimed in. I just checked the Wikipedia article on "Back in the USSR" to see what year it was released, and I found this 1984 quote from Paul McCartney.
I just liked the idea of Georgia girls and talking about places like the Ukraine as if they were California, you know? It was also hands across the water, which I'm still conscious of. 'Cause they like us out there [in Soviet Russia], even though the bosses in the Kremlin may not.
"Hands across the water" is one of McCartney's own lines, from "Uncle Albert/Admiral Halsey" (1971), but it ties in nicely with the "hands across the sea" in "Blue World."


The Arkansas/Flood connection was reinforced and expanded by another Jimmy Driftwood song, "Tennessee Stud," which I believe I first heard from the Nitty Gritty Dirt Band, although it may have been Barb and Uncle Dave again. These days my favorite rendition is Suzanna Choffel's, which captures some of the subtle unearthliness of the lyrics about a horse "the color of the sun."

The song begins thus:
Along about eighteen and twenty-five
I left Tennessee very much alive.
I never woulda got through the Arkansas mud
If I hadn't been a-ridin' on the Tennessee stud.
Why "the Arkansas mud"? Because the floodwaters have only just receded from Arkansas. Almost everything has been killed by the Flood, but the singer (presumably either Noah or one of his sons) is still "very much alive." It follows that "Tennessee" must mean the Ark and is actually "Ten-Asea" -- a reference to the eight human beings and two horses which it saved. Of course there were a lot of other animals as well, but the horses -- the Ten-Asea Stud and the Ten-Asea Mare -- were considered part of the family.


This idea of a flooded Arkansas was already firmly cemented in my mind when, in 1999, John Linnell released his solo concept album State Songs, including the astonishingly appropriate "Arkansas."

The song is about a ship called the Arkansas which is "the exact dimensions and the shape of the state whose name she bore," and the final verse asks,
When the rising tide engulfs the shore
And the waves roll over Arkansas,
Will the ship return to anchor there and replace the sunken state?
For the ship was shaped like Arkansas,
And the hull was formed without a flaw.
Every detail had been reproduced on a scale of one to one.
So once again we have Arkansas sinking beneath the waves, its place being taken by an Ark which is not in the end so different from what it is replacing.

Dice-based Scrabble

Chinese-style dice; the ace and the four always have red pips, with an extra large one for the ace

Rolling five six-sided dice (5d6) yields one of 26 possible numbers, from 5 to 30, which means it can be used as a means of randomly selecting a letter of the alphabet. Of course, the possible results of a 5d6 roll vary widely in frequency -- with, for example, 17 being 780 times as frequent as 5 -- approximating a bell curve. The letters of the alphabet also vary in frequency, though not quite so widely as 5d6 results, and not in so close an approximation of a normal distribution. Still, if the most frequent letters are mapped to the most probable 5d6 results, the results seem to be serviceable enough. Here's the key for converting numbers to letters.

And here's how the letter frequencies associated with this key match up against the actual empirical frequency of each letter in English.

Using this system, you can play (a reasonably close facsimile of) Scrabble without having a board or tiles. You just need five dice, a sheet of graph paper (with squares large enough to write in), some scrap paper, pencils, and a copy of the key. Instead of drawing tiles, roll 5d6 and jot down the the letter that corresponds to the number rolled. When you "play" a letter by writing it in a square on the graph paper, scratch it off and then roll the dice to "draw" a replacement. In a classroom setting, use a whiteboard instead of paper.

Five cornerstones

I recently received another batch of emails from a correspondent who keeps encountering repetitions of the number 5 (55, 555, etc.). This ma...